Metabolic Variability in Micro-Populations

Biological cells in a population are variable in practically every property. Much is known about how variability of single cells is reflected in the statistical properties of infinitely large populations; however, many biologically relevant situations entail finite times and intermediate-sized popul...

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Bibliographic Details
Published in:PloS one Vol. 7; no. 12; p. e52105
Main Authors: Elhanati, Yuval, Brenner, Naama
Format: Journal Article
Language:English
Published: United States Public Library of Science 27.12.2012
Public Library of Science (PLoS)
Subjects:
Adaptation, Biological
Biology
Biotechnology
Cell Physiological Phenomena
Computer Simulation
Humans
Initial conditions
Inoculum
Metabolism
Metabolites
Microfluidics
Microorganisms
Models, Theoretical
Nature
Phenotype
Population
Population (statistical)
Population Density
Population Dynamics
Population Growth
Population number
Probability theory
Properties (attributes)
Random variables
Random walk
Statistical analysis
Statistics
Stochastic models
Stochastic processes
Stochasticity
Studies
Theory
Variability
Israel
ISSN:1932-6203, 1932-6203
Online Access:Get full text
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Description
Summary:Biological cells in a population are variable in practically every property. Much is known about how variability of single cells is reflected in the statistical properties of infinitely large populations; however, many biologically relevant situations entail finite times and intermediate-sized populations. The statistical properties of an ensemble of finite populations then come into focus, raising questions concerning inter-population variability and dependence on initial conditions. Recent technologies of microfluidic and microdroplet-based population growth realize these situations and make them immediately relevant for experiments and biotechnological application. We here study the statistical properties, arising from metabolic variability of single cells, in an ensemble of micro-populations grown to saturation in a finite environment such as a micro-droplet. We develop a discrete stochastic model for this growth process, describing the possible histories as a random walk in a phenotypic space with an absorbing boundary. Using a mapping to Polya's Urn, a classic problem of probability theory, we find that distributions approach a limiting inoculum-dependent form after a large number of divisions. Thus, population size and structure are random variables whose mean, variance and in general their distribution can reflect initial conditions after many generations of growth. Implications of our results to experiments and to biotechnology are discussed.
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Conceived and designed the experiments: NB YE. Performed the experiments: NB YE. Wrote the paper: YE NB.
Competing Interests: The authors have declared that no competing interests exist.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0052105